I know Project Source makes a live-end cord kit for this unit But:WIll a different brand (which a longer cord) that is called "halo compatible" work?

First of all as I am sure you know these are designed to be direct wired to a box. As to you question, most if not all track is standard, two conductors on one side inside and one on the other. I have used different manufacturers heads on different tracks, so my belief is that they will work, unless Halo is different than everyone else. It will either fit or not.